I still can't seem to get my head around
- center of lift (which should be in the crossing of straight diagonal lines between the motors if you use the same props, right?)
- center of the "motor circle"
- center of gravity
I have never heard of the center of lift discussed in the context of a quad. In a fixed-wing, COL is important because if CG is behind COL, the plane becomes very unstable. Obviously, that doesn't apply in a quad. If the COL in a quad is dependent on the thrust developed by the motors, then it is constantly changing as the motors spin up and down. In short, I'm not sure how, or if, the concept of COL should apply to a multirotor.
Why do we care about the CG of a multirotor? One reason is that, if the CG is off-center, motors on one side will have to work harder than motors on the other side. This gives some motors less head-room to operate with, and means that the overall thrust that can be developed by the copter is limited. Consider: if the left motors have to spin at 60% to hover, and the right motors have to spin at 40%, then max thrust will be limited by the left motors. They will hit 100%, the right motors will hit 80%, and the right motors will not be able to spin up any more because the copter would begin to tilt.
By my thinking, this consideration means that the CG of the copter should be located at the centroid of the motors (center of the "motor circle") to allow all motors to run equally in hover, and to maximize the usable thrust that can be developed by the power system.
Now, what about the location of the FC? We know that the craft will tend to pivot about its CG. That's just Physics 101. So what happens if the FC is not located at the CG? Imagine that the FC is located all the way at the left side of the copter, near one of the motors. Now imagine that you roll to the left. The accelerometer in the FC will detect that the FC has dropped towards the ground and moved to the right. Take another example, where we yaw to the left. In this case, the accelerometer will detect that the FC has moved diagonally back and to the right. In short, when the FC is not located at the CG, then motions of the copter cause incorrect readings to occur in the accelerometer. The accelerometer is working correctly, but it's measuring the movement of one specific part of the copter, instead of the copter as a whole.
How does this matter? Well, first of all, if you're flying in Acro/Rate/Manual mode, I actually don't think it matters at all (someone please correct me if I'm wrong). The gyro will always read correctly, regardless of where it is located in the copter. (This ignores the issue of vibration isolation, which of course matters. Don't mount your FC at the end of one of your motor booms--duh.) Only the accelerometer will be "fooled" by mounting your FC away from your CG, and the accelerometer only comes into play when flying in an autolevel mode.
Let's elaborate on that. The FC is mounted at the end of the front-left motor boom. You yaw to the left. The accelerometer reports movement back and to the left. FC attempts to compensate by inputting right roll and front pitch. As soon as you stop yawing, the "false" accelerometer readings stop and autolevel works properly again.
Same example. You pitch forward. Accelerometer reports that the FC has moved down and backwards. FC inputs front pitch to compensate for backwards drift. If you are flying in Altitude Hold mode, then it may also throttle up to compensate for the downward movement. (My understanding is that most Alt-Hold algorithms use the accelerometer for small-scale tracking, and use GPS/Baro for elimination of accumulated error.)
What's the tl;dr? In my opinion, you should get your CG as close to the centroid of the motors as you can. But don't stress about this too much unless you are trying to maximize the maximum thrust that your copter can develop. If you seldom fly at high throttle settings, and if you seldom find yourself saying, "I need more thrust," then this is probably not a concern for you.
Likewise, you should try to place your FC as close to the CG as possible, but again, I think this seldom matters too much in real life. Most of the frames that copters use aren't large enough to get the FC far enough off-center to make it move very much. If you do some basic trig, you can calculate the length of the arc that the FC travels through when going from point A to point B on a circle of radius R, where R is the distance that the copter is from the CG. So if you imagine that the FC is 3" off of the CG and the copter rolls 10 degrees, the FC will have a "false" motion of about 1/2". Whether this ultimately matters depends on too many characteristics to list, but in many cases, it won't produce any noticeable adverse effect. Bear in mind, also, that the effect of the off-center FC will only be felt when actually inputting pitch/roll/yaw. As soon as the copter is stable (whether it's level or not), it will fly normally again.
Finally, I maintain (until proven wrong by someone smarter than me) that if you are flying in Acro/Rate/Manual mode, that FC placement doesn't matter, because the gyro is not affected by the "false" inputs caused by putting the FC away from the CG. Only FC orientation matters with the gyro (face forward) and vibration isolation.